This invention relates to apparatus for determining values of a periodic function by interpolation.
Known such apparatus comprises reading means for reading at least four values of the periodic function and converting means for converting said at least four values into a pair of derived sine and cosine functions. Interpolation values are determined by establishing the relationship between values of the sine and cosine functions at given intervals.
The reading means is only capable of reading values of the periodic function comforming to a given nominal phase separation, since it will have transducers at a given spacing from each other. Also, the interpolation is only accurate to the extent that the phase difference between the sine and cosine functions is 90.degree.. Disconformity between any actual phase separation and said given phase separation results in departure of said sine and cosine functions from said 90.degree. phase difference and in consequent inaccuracy of the interpolation. For example, such disconformity may arise if the periodicity of the periodic function does not accurately agree with the spacings of the transducers.
In known said apparatus the converting means is adapted for producing said sine and cosine functions each as a function of two said values of the periodic function. For example, if the four values are represented by signals A, B, C and D nominally in quadrature, the sine and cosine functions may be respectively derived by combining these signals as (A-C) and (B-D). This results in substantial dependence of said accuracy on said phase separation.